THE QUEST FOR THE ULTIMATE THEORY OF TIME, AN INTRODUCTION TOIRREVERSIBILITY
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From: "Juan R." González-Álvarez on 21 May 2010 12:58 ########################################################## THE QUEST FOR THE ULTIMATE THEORY OF TIME, AN INTRODUCTION TO IRREVERSIBILITY ########################################################## I do not believe that we, scientists, can develop any "ultimate theory" and I do not claim to have one. I have chosen the above title for this event, in direct relation to the last book by Sean Carroll —The quest for the ultimate theory of time— because I wanted to be a bit ironic here. I smile each occasion that arrogant string theorists talk me about their "theory of everything", specially because their approach is built over several approximations and outdated formalisms. Somehow related is the recent perplexity of mathematical physicists as John Baez who has reported his shocking finding of "a curious generalization of Hamiltonian mechanics that involves entropy" without being aware that more fundamental and elegant formalisms, as the canonical one, have been known to physical chemists and chemical physicists for more than thirty years now! My comments on entropic generalizations of mechanics are available in This Week's Finds in Mathematical Physics (Week 295). For a basic review of the outdated aspects of both string and M theory see Canonical science: its history, goals, and future. I applaud Carroll valiant attempt to consider irreversibility seriously, but his work is far from the usual standards in specialized literature. In fact, whereas several of the authors cited below have advanced our understanding of irreversibility, and some of them even provided us some irreversible equation that explains a determined range of phenomena, there is not such stuff as a Carroll equation that was used in the laboratories by us. Carroll's scientific contributions to the theory of irreversible thermodynamics, nonequilibrium statistical mechanics, or kinetic theory, are easily summarized: zero. Moreover, he is misguided on many points. I have done some comments and corrections in Carroll's blog, for instance in Chapter Eight, Chapter Eleven, Chapter Eleven (b), Chapter Twelve, Chapter Fourteen, Chapter Fourteen (b), and Chapter Fourteen (c) (external hyperlinks), but the list is far from exhaustive; what is more, I have decided to ignore both his unscientific speculations about the multiverse and its reflections on philosophy of science. The problem of the "arrow of time" is one of the oldest fundamental problems of physics. The world, as we observe around us, is irreversible: ice cubes melt and the water gets slightly cooler, broken eggs cannot be recovered, paper ages, people passes away, etc. All those observations finally led to the celebrated second law of thermodynamics, for the which no violation is known [1,2]. However, the fundamental laws of mechanics are time-reversible. There exist three attitudes toward this confrontation between mechanics and observations: the coarse-grained, the pragmatic, and the fine-grained. *The coarse-grained attitude* The authors who share this attitude affirm that, at some fundamental level, Universe is time-reversible and that irreversibility is only an illusion arising from our ignorance. This misguided attitude was initiated by Ludwig Boltzmann, who was the first who tried to obtain the second law of thermodynamics from mechanics. A short but beautiful history of the early objections that his work has raised is given in the book by Laidler, Meiser & Sanctuary [3]. For instance, the authors report how Boltzmann paper of 1877 used the probability argument, contradicting his 1872 article, and add: Much confusion resulted from the fact that for many years Boltzmann was inconsistent in his statements about the matter, sometimes using the probability argument and sometimes saying that it was not necessary to invoke probability theory. When pressed, Boltzmann invoked the probability argument to justify his arguments but sometimes insisted that he had arrived at his function H on the basis of pure dynamics. I agree with the authors that Boltzmann never understood that he had made some hidden assumptions that left out the terms that would lead to the wrong conclusions and included only the terms that led to the second law. Rather than giving the second law a purely mechanical origin, he used extra-mechanical assumptions for breaking the time-symmetry of mechanics, forcing it to match with the observations predicted by the law. As Nico G. van Kampen —considered one of the "most outstanding theoretical physicists of the second half of the 20th century" [4]— has noticed: "Obviously it is a logical impossibility to deduce from reversible equations an irreversible consequence" and emphasized that "One cannot escape from this fact by any amount of mathematical funambulism". Many important physicists, chemists, and mathematicians have stated similar views. For instance, Landau & Lifshitz speculated, in their celebrated course in theoretical physics [5], that the second law of thermodynamics would be the macroscopic form of some fundamental law of irreversibility associated to the measurement problem in quantum mechanics —recent research partially confirms their suspicion but going on the line of solving the measurement problem of quantum mechanics by using a microscopic version of the second law!—. Truesdell's criticism is much more acid and, in his classic monograph Rational thermodynamics, writes about "microscopic reversibility" in the next terms [6]: In fact, it requires no great mathematician to see that the reversibility theorem and Poincaré's recurrence theorem makes irreversible behavior impossible for dynamical systems in the classical sense. Something must be added to the dynamics of conservative systems, something not consistent with it, in order to get irreversibility at all. Everyone competent in mechanics has known this for a long time. Unfortunately, some modern physicists —especially those "who would never dream of trying to go through the mathematics and check the "proofs"", again in the acid words of Truesdell— continue to repeat both the ambiguities and subtle mistakes done by Boltzmann, and even add some recent ones. I recall that in one occasion, I was so perplexed after reading Science of Chaos or Chaos in Science? that I asked to the Nobel laureate Ilya Prigogine about his opinion; he just confirmed my findings with his concise, "the work of Bricmont is completely wrong". Unfortunately, J. Bricmont's work has been indeed influential, especially among non-experts [7]. Moreover, the amounts of "mathematical funambulism" do not seem enough and some authors are utilizing metaphysical and religious arguments to sustain their credo on coarse-graining. In a recent monograph [8], Robert Zwanzig affirms that an ice cube, melted in water, will eventually reappear, but "we never see it happen". Nevertheless, even when Zwanzig is ignoring the experimental basis of the scientific method, he is still obligated to conclude that the eventual reappearing would violate the second law of thermodynamics. It is at this point when Zwanzig reveals us the reach of his faith: "what we know about time irreversibility is obtained by experiments on a human time scale". For authors as him, the paradox of time is gone, the second law of thermodynamics, the laws of chemical kinetics, or the evolution law of biology are only illusions obtained by humans, mere mortals, whereas the time-reversible and deterministic laws of mechanics have a divine origin and thus atemporal, being valid for scales of time beyond our experience [9]! It was not my objective to give here to my readers a detailed and complete criticism of the coarse-grained attitude nor of the epistemological fallacies traditionally associated to it. I plan to write a report about all this. *The pragmatic attitude* This starts from the failure of the coarse-grained attitude. Irreversible equations of motion are postulated, which are then justified a posteriori sought in comparison with experimental data measured in the laboratory or observed in nature. This is the attitude taken by Byung Chan Eu on his interesting formulation of nonequilibrium statistical mechanics [10]: We take the viewpoint that dynamical systems consisting of 10^23 particles require dynamical equations of broken time reversal symmetry which are not derivable from the time reversal invariant Newtonian or quantum equations of motion for the systems. Another example is Zubarev's theory. He added a small infinitesimal source term to the Liouville equation, breaking its time-symmetry. The equations proposed have limited validity —for instance, the Eu equation uses a Markovian approximation— and the question of the origin of irreversibility is not even asked in this attitude. This is also the case in Lindblad's semigroup approach [11]: "Thus the present formalism has nothing to say about the origin of time's arrow". Lindblad's theory has been criticized in the basis of its original obtaining from purely mathematical assumptions and also by its detected unphysical behaviors. Recent fine-grained —see below— developments confirm the affirmations of Ulrich Weiss: "one should not attribute fundamental significance to the Lindblad master equation". In the fine grained attitude we can amend the equation with physical terms, study more general dynamical regimes, and correct Lindblad qualitative assertions about irreversibility. *The fine-grained attitude* This is the more physical, modern, and sophisticated attitude of the three. Its goal is to find the microscopic source of the irreversibility and to give a rigorous derivation of the macroscopic irreversible equations, providing us with their microscopic generalizations too. As a bonus, this attitude tries to solve other fundamental problems of physics and of philosophy, such as the problem of free-will or the problem of measurement in quantum mechanics. This attitude and the recent research advances done at this Center will be discussed in the second part: Trajectory branching in Liouville space as the source of irreversibility. *References and notes* [1] Regularly new articles are published which pretend to provide a real violation, but each time it is showed that the violation is only in the title or abstract of the articles. This was also the case for the last assertions of violations of the second law done around the year 2002. See the next reference for details. [2] Has been thermodynamics violated? 2003: CPS:physchem/0309002. González—Álvarez, Juan R. [3] The Approach to Equilibrium In Physical Chemistry 2003: Houghton Mifflin Company, Boston; 4th Ed. Laidler, Keith J.; Meiser, John H.; Sanctuary, Bryan C. [4] Nico van Kampen: charlatans beware! 2001: Physics World, January, 46. ter Haar, D. [5] Pag. 32 In Course of Theoretical Physics Volume 5, Statistical Physics Part 1 1980: Pergamon Press, Oxford; 3rd Ed; Lifshitz, E. M.; Pitaevskii, L.P. (Revision and Enlargement); Sykes, J. B.; Kearsley, M. J. (Translation from Russian). Landau, L. D.; Lifshitz, E. M. [6] Pag. 121 In Rational Thermodynamics 1968: MacGraw-Hill Book Company, New York. Truesdell, C. [7] It comes now to the mind the names Cosma Rohilla Shalizi and Carlos Zuppa, basically because both are the last authors who I read. It is rather amazing to read such misguided claims and unfair accusations against Prigogine, specially when the authority of important —fictitious— people as "Osanger [sic]", "Feymann [sic]", and "Keiser [sic]" is invoked as argument, for instance by Zuppa; which gives a good idea of the terribly ill-informed that he is. [8] The Paradoxes of Irreversibility In Nonequilibrium Statistical Mechanics 2001: Oxford Uniersity Press, Oxford. Zwanzig, Robert. [9] In their work Entropy: A dialogue, Joel L. Lebowitz & Christian Maes reproduce a conversation between a physicist and an... angel who has a perfect knowledge of the past and present state of a perfectly isolated macroscopic system of particles moving according to Hamiltonian dynamics. It is worth asking if this is the same angel who convinced Zwanzig of that the second law was obtained from experiments performed by humans and, therefore, would not be trusted. [10] Pag. 55 In Nonequilibrium Statistical Mechanics, Ensemble Method 1998: Kluwer Academic Publishers, Dordrecht. Chan Eu, Byung. [11] Pag. 19 In Non-equilibrium Entropy and Irreversibility 1983: D. Reidel Publishing Company, Dordrecht. Lindblad, Göran. ############## NEWS AND BLOG: ############## http://www.canonicalscience.org/publications/canonicalsciencetoday/canonicalsciencetoday.html http://www.canonicalscience.org/publications/canonicalsciencetoday/20100521.html -- http://www.canonicalscience.org/ BLOG: http://www.canonicalscience.org/publications/canonicalsciencetoday/canonicalsciencetoday.html
From: Hayek on 21 May 2010 16:51 Juan R. González-Álvarez wrote: > ########################################################## > THE QUEST FOR THE ULTIMATE THEORY OF TIME, AN INTRODUCTION > TO IRREVERSIBILITY > ########################################################## > > I do not believe that we, scientists, can develop any "ultimate theory" > and I do not claim to have one. I have chosen the above title for this > event, in direct relation to the last book by Sean Carroll —The quest for > the ultimate theory of time— because I wanted to be a bit ironic here. > > I smile each occasion that arrogant string theorists talk me about their > "theory of everything", specially because their approach is built over > several approximations and outdated formalisms. Somehow related is the > recent perplexity of mathematical physicists as John Baez who has reported > his shocking finding of "a curious generalization of Hamiltonian mechanics > that involves entropy" without being aware that more fundamental and > elegant formalisms, as the canonical one, have been known to physical > chemists and chemical physicists for more than thirty years now! > > My comments on entropic generalizations of mechanics are available in This > Week's Finds in Mathematical Physics (Week 295). Do you have a link for this ? TIA. I was on Sean Carroll's website, and I am completely underwhelmed. It so happens that a week or five ago, I found the real solution for the Arrow of Time, and it is in fact so death simple that it is utterly boring. I am working on the text, and hope to submit it to nature this weekend. Like you know very well, Juan, it is likely to be refused, as most good ideas are refused by peer review journals, the best examples of this I read on your website. my most sincere regards, Uwe Hayek. > For a basic review of the > outdated aspects of both string and M theory see Canonical science: its > history, goals, and future. -- We are fast approaching the stage of the ultimate inversion : the stage where the government is free to do anything it pleases, while the citizens may act only by permission; which is the stage of the darkest periods of human history. -- Ayn Rand I predict future happiness for Americans if they can prevent the government from wasting the labors of the people under the pretense of taking care of them. -- Thomas Jefferson. Socialism is a philosophy of failure, the creed of ignorance, and the gospel of envy, its inherent virtue is the equal sharing of misery. -- Winston Churchill.
From: "Juan R." González-Álvarez on 24 May 2010 10:28 Hayek wrote on Fri, 21 May 2010 22:51:00 +0200: > Juan R. González-Álvarez wrote: >> ########################################################## THE QUEST >> FOR THE ULTIMATE THEORY OF TIME, AN INTRODUCTION TO IRREVERSIBILITY >> ########################################################## >> >> I do not believe that we, scientists, can develop any "ultimate theory" >> and I do not claim to have one. I have chosen the above title for this >> event, in direct relation to the last book by Sean Carroll —The quest >> for the ultimate theory of time— because I wanted to be a bit ironic >> here. >> >> I smile each occasion that arrogant string theorists talk me about >> their "theory of everything", specially because their approach is built >> over several approximations and outdated formalisms. Somehow related is >> the recent perplexity of mathematical physicists as John Baez who has >> reported his shocking finding of "a curious generalization of >> Hamiltonian mechanics that involves entropy" without being aware that >> more fundamental and elegant formalisms, as the canonical one, have >> been known to physical chemists and chemical physicists for more than >> thirty years now! >> >> My comments on entropic generalizations of mechanics are available in >> This Week's Finds in Mathematical Physics (Week 295). > > Do you have a link for this ? Both the news and the blog links given in my original message have the direct link to n-category. However, I repeat it here: http://golem.ph.utexas.edu/category/2010/04/this_weeks_finds_in_mathematic_56.html#c032928 > TIA. > > I was on Sean Carroll's website, and I am completely underwhelmed. I also gave links with correction to several misguided claims in Carroll's book. (...) -- http://www.canonicalscience.org/ BLOG: http://www.canonicalscience.org/publications/canonicalsciencetoday/canonicalsciencetoday.html
From: "Juan R." González-Álvarez on 24 May 2010 10:32 G. L. Bradford wrote on Sat, 22 May 2010 15:06:20 -0400: > "Juan R. González-Álvarez" <nowhere(a)canonicalscience.com> wrote in > message news:pan.2010.05.21.17.03.13(a)canonicalscience.com... >> ########################################################## THE QUEST >> FOR THE ULTIMATE THEORY OF TIME, AN INTRODUCTION TO IRREVERSIBILITY >> ########################################################## >> >> > (snip) > > ================= Apart from snipping all my message (including links and references to textbooks and monographs) you submit a lot of NONSENSE, without even noticing that the general theory of irreversibility promised in the message is valid for generalied dynamical regimes where the concepts of "horizon", "singularity", and "collapse" do not apply... -- http://www.canonicalscience.org/ BLOG: http://www.canonicalscience.org/publications/canonicalsciencetoday/canonicalsciencetoday.html
From: "Juan R." González-Álvarez on 25 May 2010 05:45
G. L. Bradford wrote on Tue, 25 May 2010 03:46:07 -0400: > "Juan R. González-Álvarez" <nowhere(a)canonicalscience.com> wrote in > message news:pan.2010.05.24.14.37.53(a)canonicalscience.com... >> G. L. Bradford wrote on Sat, 22 May 2010 15:06:20 -0400: >> >>> "Juan R. González-Álvarez" <nowhere(a)canonicalscience.com> wrote in >>> message news:pan.2010.05.21.17.03.13(a)canonicalscience.com... >>>> ########################################################## THE QUEST >>>> FOR THE ULTIMATE THEORY OF TIME, AN INTRODUCTION TO IRREVERSIBILITY >>>> ########################################################## >>>> >>>> >>> (snip) >>> >>> ================= >> >> Apart from snipping all my message (including links and references to >> textbooks >> and monographs) you submit a lot of NONSENSE, without even noticing >> that the >> general theory of irreversibility promised in the message is valid for >> generalied >> dynamical regimes where the concepts of "horizon", "singularity", and >> "collapse" do >> not apply... >> >> -- > > ================== > > What you pushed out front was "The Ultimate Theory Of Time." An > instant > later that was not at all what you were delivering. Believe it or not, but reading is fundamental when replying messages in USENET... At the start of my message (that you sniped) it was done clear that there is not ultimate theory of anything, and that the chosen title was *ironic*, in direct reference to the last book by Sean Caroll, who laughdably claim to be searching for a ultimate theory of time (without even knowning the basic stuff, as the definition of entropy or evolution parameter :-) -- http://www.canonicalscience.org/ BLOG: http://www.canonicalscience.org/publications/canonicalsciencetoday/canonicalsciencetoday.html |